Problem #42




If you draw all of the diagonals in a hexagon and no three diagonals meet at a point (as would occur if, for example, the hexagon were regular), then the diagonals divide the hexagon into 25 regions as shown above.

This month's question is: if you draw all of the diagonals in a dodecagon (12-sided polygon) and no three diagonals meet at a point, how many regions do the diagonals create?



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